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Integral bases for certain TQFT-modules of the torus

Published online by Cambridge University Press:  01 November 2007

KHALED QAZAQZEH
KHALED QAZAQZEH*
Affiliation:
Department of Mathematics, Yarmouk University, Irbid 21163, Jordan. email: qazaqzeh@math.lsu.edu
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Abstract

We find two bases for the lattices of the SU(2)-TQFT-theory modules of the torus over given rings of integers. One basis is a variation on the bases defined in [GMW] for the lattices of the SO(3)-TQFT-theory modules of the torus. Moreover, we discuss the quantization functors (Vp, Zp) for p = 1, and p = 2. Then we give concrete bases for the lattices of the modules in the 2-theory. We use the above results to discuss the ideal invariant defined in [FK]. The ideal can be computed for all the 3-manifolds using the 2-theory, and for all 3-manifolds with torus boundary using the SU(2)-TQFT-theory. In fact, we show that this ideal using the SU(2)-TQFT-theory is contained in the product of the ideals using the 2-theory and the SO(3)-TQFT-theory under a certain change of coefficients, and with equality in the case of torus boundary.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 143 , Issue 3 , November 2007 , pp. 669 - 684
Copyright
Copyright © Cambridge Philosophical Society 2007

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